CHAPTER 416: CHAPTER 141 YES, THAT’S HOW IT IS! _2

Tan Lu Yuan asked again.

Qiao Yu looked up at the ceiling, he even felt that Tan Lu Yuan was testing for stupidity.

Fortunately, Qiao Xi had no hesitation and answered immediately: "There should be two paths, namely ABCA and ACDA."

"Hmm, not bad, not bad. How about I propose a question? Just answer it if you feel like it."

Yuan Zhengxin, who had been quietly listening on the side, seemed suddenly interested and interjected: "Consider an irregular decahedron, with each face being an irregular triangle.

Knowing that this decahedron has only seven vertices, the question is how many edges does it have, and if possible, summarize the adjacency relationship of each face."

This time, Qiao Xi thought for a while before answering: "I think it has fifteen edges? As for the adjacency relationship, since each face of the decahedron is triangular, each face should have an adjacency relationship with another three faces."

Alright, Qiao Yu realized he was concerned to a fault.

Elder Yuan was probably in cahoots with that Professor Tan.

Although these questions are simple, and the concepts they’re testing aren’t complex, they don’t even involve any advanced mathematical knowledge.

But what they test is basically the same. All are abstract thinking and spatial imagination.

Coming up with these questions in a short time seems quite commendable.

Qiao Xi indeed did not disappoint him; the answers were correct. At least in his view, they were correct.

As expected, he was indeed a bit green. Although he thought Qiao Xi definitely had a knack for mathematics, he didn’t expect to test it in such a simple manner.

"Qiao Xi, your situation is quite interesting. I bet you never get lost."

After hearing Qiao Xi’s answer, Elder Yuan laughed as well, providing an evaluation.

Qiao Xi nodded, fully agreeing with that point.

"Yes, in our family, only Qiao Yu’s grandmother has no sense of direction, always unable to determine directions. The rest of us have a good sense of direction. Once we’ve been somewhere, we can definitely find our way back."

Elder Yuan smiled, seriously analyzing: "Right, both you and Qiao Yu have strong spatial imagination. This indeed is a rare talent. Having a strong spatial imagination, when engaging with abstract algebra and geometry, often leads to twice the result with half the effort.

Especially when it comes to concepts like gradient, divergence, and curl in higher dimensions, and when you need to conduct optimization analysis, this ability can help you quickly understand the essence of problems.

This is also why you are more interested in Linear Algebra. The introductory content of Linear Algebra is actually more abstract compared to introductory Calculus.

But if you delve into multivariable calculus, you’ll find these pieces of knowledge quite interesting and closely related. So there’s absolutely no need to doubt yourself for not getting a perfect score on high school exams.

After all, the focus of exams varies at different stages, and high school is more application-oriented. I suppose you’ve found topics like functions, geometry, and sequences relatively easy in high school.

Meanwhile, you probably find repetitive calculations tedious, which I think is why it’s hard for you to get a perfect score in high school exams."

Qiao Xi furrowed her brow slightly, starting to recall things from high school, it’s been a while...

Qiao Yu gave Qiao Xi a subtle kick.

The two were really familiar with each other.

Qiao Yu knew that whenever Qiao Xi showed this expression, it wouldn’t be long before her attention started to waver, and then she’d zone out.

Without a reminder from someone, or without an alarm, this state would generally last for several minutes...

Qiao Xi looked at Qiao Yu, then turned to see Elder Yuan still smiling, smiled apologetically, and replied: "Hmm, possibly. I haven’t really paid much attention to these things."

"It’s not possible; it certainly is the case. Just like how you can understand Schulz’s paper."

After making the statement confidently, Yuan Zhengxin paused before asking: "Since you have insight into Schulz’s paper, you should understand concepts like metric space, density, completeness, and Cauchy sequences, right?"

Qiao Xi nodded slightly, saying: "At first, I didn’t understand. But whenever I encountered unfamiliar concepts, I would research them, and gradually I began to understand."

"That works, then. I’ll pose a question, you don’t need to prove it; just tell me if your first instinct is that the proposition is true or false."

Elder Yuan continued.

Qiao Xi lightly nodded once more.

"Suppose (X,d) is a metric space, and Y⊆X is a dense subset. If we assume Y is a complete space, then X is also a complete space. Do you think this proposition is correct?"

Qiao Xi thought for two seconds, then gently shook her head, answering: "I feel it’s incorrect."

Yuan Zhengxin laughed more heartily: "See, this is that enviable ability I talked about. Truly, both you and Qiao Yu have a natural sensitivity to mathematics. What is talent? This is it!"

After speaking, Elder Yuan glanced at Qiao Yu and continued: "Yan Zhen mentioned it to me. He said Qiao Yu once complained to him that the CMO competition problems lack elegance, and this is precisely the reason.

The most fundamental element of mathematics is the exploration and expression of patterns. The patterns here differ from physical laws; they are not swayed by the real world but are entirely constructed by mathematicians themselves.

Therefore, for people like you, you tend not to appreciate those cumbersome techniques and calculations. Because you can see the fundamental patterns more easily than others.

The human brain instinctively tires of things it doesn’t like. This is also why you two can understand Schulz’s paper only by grasping the basic concepts."